• ← MapAt
• → MapThread

MapIndexed

WMA link

MapIndexed[f, expr]

applies f to each part on the first level of expr, including the part positions in the call to f.

MapIndexed[f, expr, levelspec]

applies f to each level specified by levelspec of expr.

• • MapIndexed[f, {a, b, c}]

Include heads (index 0):

• • MapIndexed[f, {a, b, c}, Heads->True]

Map on levels 0 through 1 (outer expression gets index {}):

• • MapIndexed[f, a + b + c * d, {0, 1}]

Get the positions of atoms in an expression (convert operations to List first
to disable Listable functions):

• • expr = a + b * f[g] * c ^ e;

• • listified = Apply[List, expr, {0, Infinity}];

• • MapIndexed[#2 &, listified, {-1}]

Replace the heads with their positions, too:

• • MapIndexed[#2 &, listified, {-1}, Heads -> True]

The positions are given in the same format as used by Extract.
Thus, mapping Extract on the indices given by MapIndexed re-constructs the original expression:

• • MapIndexed[Extract[expr, #2] &, listified, {-1}, Heads -> True]